Question

How to obtain $\sqrt{5}$ (without a calculator) using complex numbers & roots of unity?

score 337 · Answer 1 · 2026-04-08 16:54:18

337

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How to obtain $\sqrt{5}$ (without a calculator) using complex numbers & roots of unity?

Published on 08 Apr 2026 - 16:54

score 131 · Answer 2 · 2026-04-13 23:32:50

131

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Radical of Polynomial Quotient Ring

Published on 13 Apr 2026 - 23:32

score 158 · Answer 3 · 2026-04-16 07:43:33

158

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Finding $n$ such that $\frac{n+1}{n}$ < $\frac{\sqrt[n+1]{(n+1)!}}{\sqrt[n]{n!}}$

Published on 16 Apr 2026 - 7:43

score 96 · Answer 4 · 2026-04-15 18:04:21

96

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If $x=\frac12(\sqrt[3]{2009}-\frac{1}{\sqrt[3]{2009}})$, what is the value of $(x+\sqrt{1+x^2})^3$?

Published on 15 Apr 2026 - 18:04

score 119 · Answer 5 · 2026-04-10 11:12:02

119

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How to determine what integer value of $j$ returns an integer when plugged in to $\sqrt{5j + 1}$ without trial and error?

Published on 10 Apr 2026 - 11:12

score 95 · Answer 6 · 2026-04-10 09:18:15

95

Views

finding complex zeros of a square root algebraic expression

Published on 10 Apr 2026 - 9:18

score 92 · Answer 7 · 2026-04-14 15:57:43

92

Views

Simple square and square root problem gives different result depending on how it is solved?

Published on 14 Apr 2026 - 15:57

score 134 · Answer 8 · 2026-04-16 11:05:12

134

Views

Use examples to explain why $\sqrt x \cdot \sqrt x=-x$ for all negative values of $x$

Published on 16 Apr 2026 - 11:05

score 140 · Answer 9 · 2026-03-25 06:02:32

140

Views

How to interpret an expression when the radical doesn't extend over anything?

Published on 25 Mar 2026 - 6:02

score 252 · Answer 10 · 2026-04-16 02:11:58

252

Views

How does $\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}$ become $\sqrt{2(2+\sqrt{2})}$?

Published on 16 Apr 2026 - 2:11

score 75 · Answer 11 · 2026-03-25 16:40:13

75

Views

Can Kummer theory - there exists some $\gamma$, $L=K(\gamma^{1/n})$ - really be applied to any abelian extension $L/K$ (in characteristic zero, say)?

Published on 25 Mar 2026 - 16:40

score 130 · Answer 12 · 2026-04-13 02:47:07

130

Views

Show that $a^3+5a$ is an integer

Published on 13 Apr 2026 - 2:47

score 67 · Answer 13 · 2026-04-14 22:19:53

67

Views

Evaluating $\sqrt[3]{100^2\cdot 97+299}$ with clever algebra

Published on 14 Apr 2026 - 22:19

score 255 · Answer 14 · 2026-04-15 04:23:44

255

Views

Calculate the sum of $\left\lfloor \sqrt{k} \right\rfloor$

Published on 15 Apr 2026 - 4:23

score 758 · Answer 15 · 2026-04-17 15:58:58

758

Views

Prove if $\sqrt{x+1}+\sqrt{y+2}+\sqrt{z+3}=\sqrt{y+1}+\sqrt{z+2}+\sqrt{x+3}=\sqrt{z+1}+\sqrt{x+2}+\sqrt{y+3}$, then $x=y=z$.

Published on 17 Apr 2026 - 15:58

List Question

How to obtain $\sqrt{5}$ (without a calculator) using complex numbers & roots of unity?

Radical of Polynomial Quotient Ring

Finding $n$ such that $\frac{n+1}{n}$ < $\frac{\sqrt[n+1]{(n+1)!}}{\sqrt[n]{n!}}$

If $x=\frac12(\sqrt[3]{2009}-\frac{1}{\sqrt[3]{2009}})$, what is the value of $(x+\sqrt{1+x^2})^3$?

How to determine what integer value of $j$ returns an integer when plugged in to $\sqrt{5j + 1}$ without trial and error?

finding complex zeros of a square root algebraic expression

Simple square and square root problem gives different result depending on how it is solved?

Use examples to explain why $\sqrt x \cdot \sqrt x=-x$ for all negative values of $x$

How to interpret an expression when the radical doesn't extend over anything?

How does $\sqrt{2+\sqrt{2}}+\sqrt{2-\sqrt{2}}$ become $\sqrt{2(2+\sqrt{2})}$?

Can Kummer theory - there exists some $\gamma$, $L=K(\gamma^{1/n})$ - really be applied to any abelian extension $L/K$ (in characteristic zero, say)?

Show that $a^3+5a$ is an integer

Evaluating $\sqrt[3]{100^2\cdot 97+299}$ with clever algebra

Calculate the sum of $\left\lfloor \sqrt{k} \right\rfloor$

Prove if $\sqrt{x+1}+\sqrt{y+2}+\sqrt{z+3}=\sqrt{y+1}+\sqrt{z+2}+\sqrt{x+3}=\sqrt{z+1}+\sqrt{x+2}+\sqrt{y+3}$, then $x=y=z$.

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